derivative h(x)=sqrt(3+5sin(x))

解答

导数

h (x) = 3 + 5 sin (x)

\frac{5 cos ( x )}{2 3 + 5 sin ( x )}

求解步骤

\frac{d}{d x} (3 + 5 sin (x))

使用连锁律:

\frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

= \frac{1}{2 3 + 5 sin ( x )} \frac{d}{d x} (3 + 5 sin (x))

\frac{d}{d x} (3 + 5 sin (x)) = 5 cos (x)

= \frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x)

化简

\frac{1}{2 3 + 5 sin ( x )} \cdot 5 cos (x) : \frac{5 cos ( x )}{2 3 + 5 sin ( x )}

= \frac{5 cos ( x )}{2 3 + 5 sin ( x )}

\int_{- 4}^{1} \frac{1}{x ^{4}} d x

\int_{- 2}^{- 1} (4 y^{3} + \frac{2}{y ^{3}}) d y

l a pl a ce t r an s f or m 4 t^{4}

\frac{d}{d x} (\frac{x ^{n}}{( 1 + x ) ^{n}})

\frac{d}{d x} (ln (x) - x)